Practice on the area of a trapezoid

### 1.1. Solve the exercises in the textbook Practice page 94

**Lesson 1 Textbook page 94**

Find the area of a trapezoid whose base lengths are a and b, and height h

a) a = 14cm; b = 6cm; h = 7cm

b) \(a = \frac{2}{3}m;{\mkern 1mu} {\kern 1pt} b = \frac{1}{2}m;{\mkern 1mu} {\kern 1pt} h = \frac{9}{4}m\)

c) a = 2.8m; b = 1.8m; h = 0.5m

__Solution guide:__

a) The area of the trapezoid is:

\(\frac{{(14 + 6) \times 7}}{2} = 70(c{m^2})\)

b) The area of the trapezoid is:

\(\frac{{\left( {\frac{2}{3} + \frac{1}{2}} \right) \times \frac{9}{4}}}{2} = \frac{ {21}}{{16}} = 1.3125({m^2})\)

c) The area of the trapezoid is:

\(\frac{{(2.8 + 1.8) \times 0.5}}{2} = \frac{{23}}{{20}} = 1.15({m^2})\ )

Lesson 2 Textbook page 94

A trapezoidal field has a large bottom 120m, a small bottom equal to \(\frac{2}{3}\) a large bottom. Baby bottom is 5m longer than height. Average every 100m^{2} harvested 64.5 kg of rice. Calculate the number of kilograms of rice harvested in that field.

__Solution guide:__

The small bottom of a trapezoidal field is:

\(120 \times \frac{2}{3} = 80\left( m \right)\)

The height of the trapezoidal field is:

80 – 5 = 75 (m)

The area of a trapezoidal field is:

\(\frac{{(120 + 80) \times 75}}{2} = 7500({m^2})\)

7500m^{2} fold 100 m^{2}: 7500 : 100 = 75 (times)

The number of rice harvested in the field is:

64.5 x 75 = 4837.5 (kg)

Answer: 4837.5 (kg)

Lesson 3 Textbook page 94

Correct write D, false write S:

a) Areas of trapezoids AMCD, MNCD, NBCD are equal

b) The area of trapezoid AMCD is \(\frac{1}{3}\) the area of rectangle ABCD.

__Solution guide:__

a) Write the letter D in the blank box.

Three trapezoids AMCD, MNCD, NBCD have equal areas because they have a common base DC, a small base equal to 3cm and have the same height, which is the length of the line segment AD.

b) Write the letter S in the blank:

Area of rectangle ABCD is: AB × AD = 9 × AD

The area of trapezoid AMCD is equal to:

\(\frac{{(DC + AM) \times AD}}{2} = \frac{{(9 + 3) \times AD}}{2} = 6 \times AD\)

We have: \(\frac{{6 \times AD}}{{9 \times AD}} = \frac{6}{9} = \frac{2}{3}\)

So the area of trapezoid AMCD is 2/3 of the area of rectangle ABCD.

## 1.2. Solving exercises in textbooks General practice page 95

**Lesson 1 Textbook page 95**

Find the area of a right triangle with the lengths of the two sides:

a) 3cm and 4cm

b) 2.5m and 1.6m

c) \(\frac{2}{5}\)dm and \(\frac{1}{6}\) dm.

__Solution guide:__

a) The area of a right triangle is:

\(\frac{{3 \times 4}}{2} = 6\:(c{m^2})\)

b) The area of a right triangle is:

\(S = \frac{{2,5 \times 1.6}}{2} = 2\:({m^2})\)

c) The area of a right triangle is:

\(S = \frac{{\frac{2}{5} \times \frac{1}{6}}}{2} = \frac{1}{{30}}\:(d{m^2 })\)

Lesson 2 Textbook page 95

By how many square centimeters is the area of trapezoid ABED larger than the area of triangle BEC ?

__Solution guide:__

Trapezoid ABED has a small base AB and a large base DE, height AH.

The area of trapezoid ABED is:

\(\frac{{(2,5 + 1.6) \times 1,2}}{2} = 2.46\:(d{m^2})\)

The height of triangle BEC is equal to the length of segment AH and is equal to 1.2dm

The area of triangle BEC is:

\(\frac{{1,3 \times 1,2}}{2} = 0.78\:(d{m^2})\)

The area of trapezoid ABED is larger than the area of triangle BEC in square decimeters:

2.46 − 0.78 = 1.68(dm^{2})

Answer: 1.68(dm^{2})

Lesson 3 Textbook page 95

On a trapezoidal garden plot (as shown in the figure), people use 30% of the land for growing papaya and 25% of the area for growing bananas.

a) Ask how many papaya trees can be planted, knowing that each papaya tree needs 1.5m^{2} land?

b) Ask how many more banana trees can be planted than papaya trees, knowing that each banana tree needs 1m^{2} land?

__Solution guide:__

The area of a trapezoidal garden is:

\(\frac{{(70 + 50) \times 40}}{2} = 2400\:({m^2})\)

The papaya planting area is:

2400 : 100 x 30 = 720 (m2)

Banana growing area is:

2400:100 × 25 = 600 (m2)

The number of papaya trees planted is:

720 : 1.5 = 480 (tree)

b) The number of banana trees that can be planted is:

600 : 1 = 600 (tree)

The number of banana trees planted more than the number of papaya trees is:

600 – 480 = 120 (tree)

Answer: a) 480 trees;

b) 120 trees.

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